1.1 2D Points

8.12

1.1 2D Points🔗ℹ

package: euclid

A 2D point is an exact location in the Euclidean plane, and has no length, width, or thickness.

struct
(struct point (x y)
    #:transparent)
  x : (and/c real? (not/c infinite?) (not/c nan?))
  y : (and/c real? (not/c infinite?) (not/c nan?))

A 2D point structure with coordinates x and y.

value
origin : point? = (point 0 0)

The origin, which is the point located at coordinates (0,0).

procedure
(point-add p ...) → point?
p : point?

Adds each p together and returns a point representing their sum.

Example:

> (point-add (point 2 3) (point 1 5))
(3,8)

procedure
(point-sum points) → point?
points : (sequence/c point?)

Returns the sum of points.

Example:

> (point-sum (list (point 1 1) (point 2 2) (point 3 3)))
(6,6)

value
into-point-sum : (reducer/c point? point?)

A reducer that adds together a sequence of points.

Example:

> (transduce (in-range 0 5)
(mapping (λ (x) (point x 0)))
#:into into-point-sum)
(10,0)

procedure
(point-distance p q) → (and/c (>=/c 0) (not/c infinite?))
p : point?
q : point?

Returns the distance between p and q.

Example:

> (point-distance (point 1 1) (point 4 5))
5

1.1.1 2D Polar Coordinates🔗ℹ

procedure
(polar-point radius azimuth) → point?
radius : (and/c (>=/c 0) (not/c infinite?))
azimuth : angle?

Constructs a point represented by the polar coordinates radius and azimuth, where radius is the point’s distance from the origin and azimuth is the angle of direction from the origin.

Examples:

> (polar-point 6 (degrees 0))
(6,0)
> (polar-point 6 (degrees 30))
(5.196152422706632,3)
> (polar-point 6 (degrees 45))
(4.242640687119285,4.242640687119285)
> (polar-point 6 (degrees 60))
(3,5.196152422706632)
> (polar-point 6 (degrees 90))
(0,6)

procedure
(polar-point-radius p) → (and/c (>=/c 0) (not/c infinite?))
p : point?

Returns the distance from the origin to p.

Examples:

> (polar-point-radius (point 3 4))
5
> (polar-point-radius (point 10 0))
10

procedure
(polar-point-azimuth p) → angle?
p : point?

Returns the angle of direction from the origin to p. If p is the origin, then an angle of zero degrees is returned.

Examples:

> (polar-point-azimuth (point 5 0))
0°
> (polar-point-azimuth (point 5 5))
45°
> (polar-point-azimuth (point 0 5))
90°

1.1	2D Points
1.2	Angles
1.3	2D Rays